Problem: Solve for $x$ and $y$ using elimination. ${5x+5y = 45}$ ${6x-3y = 9}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-6$ and the bottom equation by $5$ ${-30x-30y = -270}$ $30x-15y = 45$ Add the top and bottom equations together. $-45y = -225$ $\dfrac{-45y}{{-45}} = \dfrac{-225}{{-45}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {5x+5y = 45}\thinspace$ to find $x$ ${5x + 5}{(5)}{= 45}$ $5x+25 = 45$ $5x+25{-25} = 45{-25}$ $5x = 20$ $\dfrac{5x}{{5}} = \dfrac{20}{{5}}$ ${x = 4}$ You can also plug ${y = 5}$ into $\thinspace {6x-3y = 9}\thinspace$ and get the same answer for $x$ : ${6x - 3}{(5)}{= 9}$ ${x = 4}$